tv does not detect my macbook air when connected to mini display to

i bought a good quality mini display to hdmi adapter from blue rigger amazon. connected my mid 2012 model of macbook air to samsung LA26B350 lcd tv but the display is not detecting in the lcd tv. when i connect the adapter the display arrangement tab is missing. Tried pressing the option key on mac and detecting the display but nothing happens. My samsung tv resolution is 1366*768 which is i think half hd. Do i require the full hd tv to connect my mac to lcd tv? please help if any solutions. should i try using mini display to vga adapter?